Test: Network Theorems (A.C.) - 2 - Electrical Engineering (EE) MCQ

Solution:

Thevenin Voltage Calculation:

- First, we need to find the Thevenin equivalent circuit for the given circuit.
- Remove the load resistor (RL) from the circuit.
- Calculate the equivalent resistance (Rth) looking back into the circuit.
- Calculate the open-circuit voltage (Voc) which is the Thevenin voltage.

Calculations:

- The Thevenin resistance (Rth) can be calculated by shorting all the independent sources and then finding the equivalent resistance looking back into the circuit.
- By shorting the voltage source, the circuit reduces to a simple resistive network, and Rth can be calculated.
- Once Rth is calculated, the next step is to find the open-circuit voltage (Voc) which is the Thevenin voltage.
- The Thevenin voltage can be calculated by finding the voltage across the terminals where the load resistor was connected with RL removed.
- The Thevenin voltage is the voltage between those two terminals.

Final Answer:

- The Thevenin voltage as seen by RL is 5.74 ∠-16.7° V.

The voltage at node A in the figure is
(V - 20)/20 + (V - 10)/10 + V/2 = 0
⇒ V = 3.07V. Now short circuiting 10V source,

(V - 20)/20 + V/2 + V/10 = 0
⇒ V = 1.5V.

To find R_th, two voltage sources are removed and replaced with short circuit. The resistance at terminals AB then is the parallel combination of the 10Ω resistor and 5Ω resistor

⇒ R_th=(10 × 5)/15 = 3.33Ω.

The magnitude of the current in Norton’s equivalent circuit is equal to the current passing through the short circuited terminals that are I = 20/5 = 4A.